Question

1. triangle stu is dilated to create triangle stu using the origin as the center of dilation. which one of the following statements is true? a triangle stu is dilated by a scale factor of 1/4 to create triangle stu. b triangle stu is dilated by a scale factor of 1/2 to create triangle stu. c triangle stu is dilated by a scale factor of 4 to create triangle stu. d triangle stu is dilated by a scale factor of 2 to create triangle stu.

Explanation:

Step1: Identify side - length relationship

Let's consider a side - length of the original triangle $\triangle STU$ and the dilated triangle $\triangle S'T'U'$. For example, if we look at the horizontal distance between two corresponding vertices. Suppose we consider the $x$ - coordinates of corresponding vertices. Let's assume a vertex of $\triangle STU$ and its corresponding vertex of $\triangle S'T'U'$. If we take a side of $\triangle STU$ and its corresponding side of $\triangle S'T'U'$, we can see that the side - lengths of $\triangle S'T'U'$ are half of the side - lengths of $\triangle STU$.

Step2: Recall dilation formula

The scale factor $k$ of a dilation with the origin as the center of dilation is given by the ratio of the coordinates of the image to the coordinates of the pre - image. If $(x,y)$ is a point on the pre - image and $(x',y')$ is the corresponding point on the image, then $x'=kx$ and $y' = ky$. When the image is smaller than the pre - image, $0

Answer:

A. Triangle STU is dilated by a scale factor of $\frac{1}{2}$ to create triangle S'T'U'